HSBC has published a full-page advert containing an apology in several newspapers, over claims that its Swiss private bank helped clients evade tax.
The advert reproduces an open letter signed by chief executive Stuart Gulliver, which says recent coverage had been "a painful experience".
Whistleblower Herve Falciani has said the UK government should have known about the scandal in 2010.
The UK's Treasury Committee is to conduct an inquiry into the claims.
And HM Revenue & Customs met the police and the Serious Fraud Office this week to expand the scope of its investigation into Swiss tax accounts held with HSBC.
MPs have accused tax officials of failing to deal with the matter adequately.
Mr Gulliver, whose letter is addressed to the bank's customers and staff, said in his letter that he wanted to reassure customers that its Swiss private bank had been "completely overhauled".
"The media focus has been on historical events that show the standards to which we operate today were not universally in place in our Swiss operations eight years ago.
"We must show we understand that the societies we serve expect more from us. We therefore offer our sincerest apologies."
Mr Gulliver also said that the recent media coverage must be put "into context".
"A former employee of the Swiss private bank stole data more than eight years ago.
"Major UK media outlets have focused on approximately 140 names included in the stolen data.
"Many of the people mentioned have been named simply because they are well-known individuals. The vast majority of these 140 people are no longer clients.
"The media has been mentioning a number of 100,000 clients. At its peak, the Swiss private bank had about 30,000 accounts.
"We have absolutely no appetite to do business with clients who are evading their taxes or who fail to meet our financial crime compliance standards."
Mr Falciani also said French authorities had got in touch with HMRC and passed on information about the bank's activities in 2010, and that the UK government should have known the bank itself was doing wrong at that time.
Lin Homer, the chief executive of HMRC, has told MPs why there had been only one prosecution of someone whose hidden accounts in Switzerland had been revealed.
She said that most of the information leaked in 2010, which involved about 3,600 UK individuals, was incomplete or "dirty" data.
Of these, 3,200 individuals had been traced and, of the 1,100 most serious cases - which HMRC had chosen to pursue - only 130 were now outstanding.
From the rest of those cases, £135m had been recovered, Ms Homer said.
She also said that two-thirds of the total group of UK-based HSBC account holders "were found to be compliant" with UK tax rules, in some cases because they had non-dom status.